Skip to main content

An Algorithm to Discover the k-Clique Cover in Networks

  • Conference paper
Progress in Artificial Intelligence (EPIA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5816))

Included in the following conference series:

Abstract

In social network analysis, a k-clique is a relaxed clique, i.e., a k-clique is a quasi-complete sub-graph. A k-clique in a graph is a sub-graph where the distance between any two vertices is no greater than k. The visualization of a small number of vertices can be easily performed in a graph. However, when the number of vertices and edges increases the visualization becomes incomprehensible. In this paper, we propose a new graph mining approach based on k-cliques. The concept of relaxed clique is extended to the whole graph, to achieve a general view, by covering the network with k-cliques. The sequence of k-clique covers is presented, combining small world concepts with community structure components. Computational results and examples are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Alba, R.D.: A graph-theoretic definition of a sociometric clique. Journal of Mathematical Sociology 3, 113–126 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  2. Berners-Lee, T.: The Next Wave of the Web: Plenary Panel. In: 15th International World Wide Web Conference, WWW2006, Edinburgh, Scotland (2006)

    Google Scholar 

  3. Cavique, L., Luz, C.: A Heuristic for the Stability Number of a Graph based on Convex Quadratic Programming and Tabu Search, special issue of the Journal of Mathematical Sciences, Aveiro Seminar on Control Optimization and Graph Theory, Second Series (to appear, 2009)

    Google Scholar 

  4. Cavique, L., Rego, C., Themido, I.: A Scatter Search Algorithm for the Maximum Clique Problem. In: Ribeiro, C., Hansen, P. (eds.) Essays and Surveys in Metaheuristics, pp. 227–244. Kluwer Academic Publishers, Dordrecht (2002)

    Chapter  Google Scholar 

  5. Chvatal, V.: A greedy heuristic for the set-covering problem. Math. Oper. Res. 4, 233–235 (1979)

    MathSciNet  MATH  Google Scholar 

  6. Cook, D.J., Holder, L.B. (eds.): Mining Graph Data. John Wiley & Sons, New Jersey (2007)

    MATH  Google Scholar 

  7. DIMACS: Maximum clique, graph coloring, and satisfiability, Second DIMACS implementation challenge (1995), http://dimacs.rutgers.edu/Challenges/ (accessed April 2009)

  8. Erdos, P., Renyi, A.: On Random Graphs. I. Publicationes Mathematicae 6, 290–297 (1959)

    MathSciNet  MATH  Google Scholar 

  9. Faloutsos, M., Faloutsos, P., Faloutsos, C.: On power-law relationships of the Internet topology. In: SIGCOMM, pp. 251–262 (1999)

    Google Scholar 

  10. Floyd, R.W.: Algorithm 97: Shortest Path. Communications of the ACM 5(6), 345 (1962)

    Article  Google Scholar 

  11. Gomes, M., Cavique, L., Themido, I.: The Crew Time Tabling Problem: an extension of the Crew Scheduling Problem. Annals of Operations Research, volume Optimization in transportation 144(1), 111–132 (2006)

    Article  MATH  Google Scholar 

  12. Grossman, J., Ion, P., Castro, R.D.: The Erdos number Project (2007), http://www.oakland.edu/enp/ (accessed April 2009)

  13. Johnson, D.S.: Approximation algorithms for combinatorial problems. Journal of Computer and System Science 9, 256–278 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  14. Kellerman, E.: Determination of keyword conflict. IBM Technical Disclosure Bulletin 16(2), 544–546 (1973)

    Google Scholar 

  15. Luce, R.D.: Connectivity and generalized cliques in sociometric group structure. Psychometrika 15, 159–190 (1950)

    Article  MathSciNet  Google Scholar 

  16. Milgram, S.: The Small World Problem. Psychology Today 1(1), 60–67 (1967)

    Google Scholar 

  17. Mokken, R.J.: Cliques, clubs and clans. Quality and Quantity 13, 161–173 (1979)

    Article  Google Scholar 

  18. Moreno, J.L.: Who Shall Survive? Nervous and Mental Disease Publishing Company, Washington DC (1934)

    Google Scholar 

  19. Scott, J.: Social Network Analysis - A Handbook. Sage Publications, London (2000)

    Google Scholar 

  20. Soriano, P., Gendreau, M.: Tabu search algorithms for the maximum clique. In: Johnson, D.S., Trick, M.A. (eds.) Clique, Coloring and Satisfiability, Second Implementation Challenge DIMACS, pp. 221–242 (1996)

    Google Scholar 

  21. Wasserman, S., Faust, K.: Social Network Analysis: Methods and Applications. Cambridge University Press, Cambridge (1994)

    Book  MATH  Google Scholar 

  22. Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393(6684), 409–410 (1998)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cavique, L., Mendes, A.B., Santos, J.M.A. (2009). An Algorithm to Discover the k-Clique Cover in Networks. In: Lopes, L.S., Lau, N., Mariano, P., Rocha, L.M. (eds) Progress in Artificial Intelligence. EPIA 2009. Lecture Notes in Computer Science(), vol 5816. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04686-5_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-04686-5_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04685-8

  • Online ISBN: 978-3-642-04686-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics